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Three sides of triangle in functional equation

Source: Iran TST 2023 ; Exam 2 Problem 3

March 15, 2023
function equationalgebrafunctional equation

Problem Statement

Find all function f:R+ā†’R+ f: \mathbb{R}^{+} \to \mathbb{R}^{+} such that for every three real positive number x,y,zx,y,z :
x+f(y),f(f(y))+z,f(f(z))+f(x) x+f(y) , f(f(y)) + z , f(f(z))+f(x)
are length of three sides of a triangle and for every postive number pp , there is a triangle with these sides and perimeter pp.
Proposed by Amirhossein Zolfaghari
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